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JEE Main 202224 JuneMorning Shift
Exam
JEE Main
Year
2022
Date
24 June
Shift
Morning Shift
Subject
Mathematics
Chapter
Complex Number

JEE Main 2022 · 24 June · Morning Shift · Mathematics · Complex Number

Let A = \ z ∈ C: 1 ⩽ |z - (1 + i)| ⩽ 2\ and B = \ z ∈ A: |z - (1 -...

Let A={z∈C:1⩽∣z−(1+i)∣⩽2}A = \left\{z \in C: 1 ⩽ \left|z - \left(1 + i\right)\right| ⩽ 2\right\} and B={z∈A:∣z−(1−i)∣=1}B = \left\{z \in A: \left|z - \left(1 - i\right)\right| = 1\right\}. Then, BBLet A = \ z ∈ C: 1 ⩽ |z - (1 + i)| ⩽ 2\ and B = \ z ∈ A: |z - (1 - i)| = 1\ . Then, B

Options

  1. Ais an empty set
  2. Bcontains exactly two elements
  3. Ccontains exactly three elements
  4. Dis an infinite set

Correct answer

D. is an infinite set

Step-by-step solution

\left|z - \left(1 + i\right)\right| = 1 \text{andand} \left|z - \left(1 + i\right)\right| = 2representstwoconcentriccircleswithcentre(1,1)represents two concentric circles with centre \left(1, 1\right).

\left|z - \left(1 - i\right)\right| = 1representsacirclewithcentre(1,−1)represents a circle with centre \left(1, - 1\right) and radius 11

Let A = \ z ∈ C: 1 ⩽ |z - (1 + i)| ⩽ 2\ and B = \ z ∈ A: |z - (1 - i)| = 1\ . Then, B

AA represents the region between the concentric circles with centre \left(1, 1\right)</p><p>Set</p><p>SetBcontainsallpointsonminorarccontains all points on minor arcPQofthecircle∣z−(1−i)∣=1of the circle \left|z - \left(1 - i\right)\right| = 1.

Hence, BB has infinite elements.

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